A052620 E.g.f. (1-x)^2/(1-3x+x^3).

1, 1, 8, 66, 768, 11040, 190800, 3845520, 88583040, 2295578880, 66098592000, 2093556326400, 72337863628800, 2707751497651200, 109153235884492800, 4714413247095552000, 217193790828478464000, 10631538129843671040000

Offset: 0

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 566

Programs

Maple

spec := [S,{S=Sequence(Prod(Z,Sequence(Z),Union(Z,Sequence(Z))))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);

Formula

E.g.f.: (-1+x)^2/(1-3*x+x^3)

Recurrence: {a(1)=1, a(0)=1, a(2)=8, (n^3+6*n^2+11*n+6)*a(n) +(-3*n-9)*a(n+2) +a(n+3)=0}

Sum(-1/9*(-1+2*_alpha^2-2*_alpha)*_alpha^(-1-n), _alpha=RootOf(1-3*_Z+_Z^3))*n!

a(n) = n!*A052545(n). - R. J. Mathar, Jun 03 2022